An airbrush was first and foremost a tool for illustrators and artists, and is capable of incredible detail in trained hands. Airbrushes can be used for "flood" coats, and pencil thin lines. Since the function of an airbrush is to atomize paint into fine particles, it can apply paint in such thin coats that you can apply shadow and shade without blocking out the layer below.
However, as with all tools they can have limitations. For instance it is difficult, though not impossible, for a modeler to use an airbrush for painting eye details on figures. A brush is a far simpler tool to use in those cases. I use a brush for touching up color or when I don't want to go through the ritual of setting the airbrush up, and cleaning it up after for a five minute paint job. Detail work like dry brushing, applying washes or dot filtering can only be done with a paintbrush.
In short I use my airbrush for the majority of my painting and use the brushes for detail work.
The consensus is that a dual action gravity fed airbrush such as the Thayer & Chandler Omni 400, Badger 100LG, Paasche Talon or Iwata HP-CS to be the best choice for both broad coverage and fine detail work.